Abstract
In a competing risks analysis, interest lies in the cause-specific cumulative incidence function (CIF) which is usually obtained in a modelling framework by either (1) transforming on all of the cause-specific hazard (CSH) or (2) through its direct relationship with the subdistribution hazard (SDH) function. We expand on current competing risks methodology from within the flexible parametric survival modelling framework (FPM) and focus on approach (2). This models all cause-specific CIFs simultaneously and is more useful when prognostic related questions are to be answered. We propose the direct FPM approach for the cause-specific CIF which models the (log-cumulative) baseline hazard without the requirement of numerical integration leading to benefits in computational time. It is also easy to make out-of-sample predictions to estimate more useful measures and alternative link functions can be incorporated, for example, the logit link. To implement the methods, a new estimation command, stpm2cr, is introduced and useful predictions from the model are demonstrated through an illustrative Melanoma dataset.
Highlights
In competing-risks analysis, researchers consider the cause-specific cumulative incidence function (CIF), which is the probability of failure of an event in the presence of other competing events
Competing-risks models are being widely applied in research, and fitting regression models on the subdistribution hazard scale is encouraged for researchers to make inferences on prognosis and understand the association of a covariate on risk
All causes are modeled simultaneously, so there is no need to fit separate models for each cause. This is implemented in the new stpm2cr command, an adaptation of the stpm2 command
Summary
In competing-risks analysis, researchers consider the cause-specific cumulative incidence function (CIF), which is the probability of failure of an event in the presence of other competing events. The preferred method for modeling covariate effects on the cause-specific CIF is the Fine and Gray (1999) model, available through the stcrreg command This approach allows us to model only one event using the partial likelihood. Jeong and Fine (2006) investigated a direct parametric inference approach and defined a likelihood that allows us to model all the cause-specific CIFs simultaneously We extend this approach to FPMs, in which it is easy to model time-dependent effects and obtain useful out-ofsample predictions. The interpretation is not as simple as modeling a single event and suffers from similar issues in interpretation as the complementary log-log link function Incorporating such alternative link functions on the cause-specific CIF is easy to implement using the approach we outline in this article. We conclude by discussing the approach’s limitations and potential extensions
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